Bladed Disk Resonance - Part 3 - Open Impellers

Covered impellers are predominately used in process gas compressors with high loading per stage. Mechanical tip speeds can be fairly low especially for high mol weight gases than give high equivalent aerodynamic tip speeds. Use of a cover disk however limits tip speed possible for some designs; open impellers prevail for applications such as plant air compressors and turbochargers, including radial turbines. Centrifugal stress limits determine if a cover can be used; however as long as possible resonance points, some of which are described below, are evaluated the cover can be eliminated. Integrally geared process compressors similar to plant-air compressors have been used more often recently as there are aerodynamic performance advantages with separately controlled stages.

The first check that should be made is to avoid disk critical speeds. As there is not a cover disk that adds more favorable stiffness to offset added mass, open impellers have lower disk mode frequencies. A typical example:

A disk critical speed for a 4-diameter mode occurred for another design causing fatigue cracks at the disk outer diameter. The excitation came from flow asymmetry due to the discharge volute, causing lower harmonic of speed excitation especially near compressor surge, so that the disk profile was changed to increase frequencies. The redesign avoided disk critical resonance with enough margins from operating speed as shown in Campbell diagram below:

Interaction resonance of disk modes based on differences between rotating and stationary blade numbers also need checked using equations or interference diagrams described in author’s previous article. Open impellers also have individual cantilevered blade modes much lower than designs where a cover gives fixed-fixed boundaries. Free standing blades are especially prone to fail with excessive compressor surging, as are axial compressors. The most responsive blade modes are designed to avoid excitation from inlet guide vanes – fixed or adjustable – and for turbines from inlet nozzles. If there is minimal mistuning for an integrally bladed disk it can cause blade modes coupled to each other in diametral patterns. Again a caution is always to avoid equal blade and vane numbers, checking inlet and diffuser vanes.

Even with a pure axial inlet without vanes, stages with a discharge volute encounter added excitation such that individual blade modes are at risk from low order harmonics of speed. Excitation increases when approaching surge and also at overload approaching choke point. Vendors set design limits as to what the lowest harmonic limit is for the fundamental blade-bending mode. The mode is such that each blade has its mistuned frequency different than others so any of the blades could be in resonance. Motor drives could have particular frequencies tuned away from resonance.

A case where a fundamental blade mode was excited causing fatigue during excessive surging is also described in the reference below. Blade resonance was acceptable under normal conditions with the Campbell Diagram below:

The high-speed, high-pressure ratio impeller was redesigned to give higher frequencies, and for ultimate reliability a special design was used to add friction damping. The blade profiles were curved with shapes for aerodynamic improvements, giving the opportunity to add damping pins in a zig-zag pattern shown below:

Radial-inflow turbines have excitation with inlet nozzles at the outer periphery so besides disk critical speeds interaction disk resonance requires checks. Individual blade modes are also checked versus number of nozzles times rotating speed. An unusual case had a second blade mode equal to the difference between numbers of two upstream excitation sources times operating speed, causing fatigue at the trailing edge. “Goodman Factor” is defined as ratio of allowable alternating stress to steady state gas load bending stress. Failure initiation location agreed with the minimum Goodman Factor for the second blade mode as shown below:

Redesign of the trailing edge portion of the blade successfully eliminated fatigue.

Article submissions to now have not covered pumps that are at lower risk due to high fluid damping. Future articles will also discuss steam turbines including need for added damping.

Ref.  Kushner, F., 2004, "Rotating Component Modal Analysis And Resonance Avoidance Recommendations", Tutorial, Proceedings of the 33rd Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX. Pp. 143-161.